On a new family of generalized Bernstein operators

Maria Talpau Dimitriu

Abstract


In this paper we remark that $\alpha$-Bernstein operators, introduced by X. Y. Chen et al., are combinations of two known operators (Stancu and Bernstein operators) and we establish the preservation of global smoothness properties by these linear operators, the global smoothness being expressed by a Lipschitz condition with a certain second order modulus of continuity.

Keywords


Bernstein-type operators; global smoothness preservation; second order modulus of continuity

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DOI: http://dx.doi.org/10.24193/subbmath.2022.3.12

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